Maximal class numbers of CM number fields
نویسندگان
چکیده
منابع مشابه
CM-fields with relative class number one
We will show that the normal CM-fields with relative class number one are of degrees ≤ 216. Moreover, if we assume the Generalized Riemann Hypothesis, then the normal CM-fields with relative class number one are of degrees ≤ 96, and the CM-fields with class number one are of degrees ≤ 104. By many authors all normal CM-fields of degrees ≤ 96 with class number one are known except for the possib...
متن کاملClass Numbers of Imaginary Abelian Number Fields
Let N be an imaginary abelian number field. We know that hN , the relative class number of N , goes to infinity as fN , the conductor of N , approaches infinity, so that there are only finitely many imaginary abelian number fields with given relative class number. First of all, we have found all imaginary abelian number fields with relative class number one: there are exactly 302 such fields. I...
متن کاملFast Computation of Relative Class Numbers of CM-Fields
It was well known that it is easy to compute relative class numbers of abelian CM-fields by using generalized Bernoulli numbers (see Theorem 4.17 in Introduction to cyclotomic fields by L. C. Washington, Grad. Texts in Math., vol. 83, Springer-Verlag, 1982). Here, we provide a technique for computing the relative class number of any CM-field. 1. Statement of the results Proposition 1. Let n ≥ 1...
متن کاملComputation of Relative Class Numbers of Cm-fields
It was well known that it is easy to compute relative class numbers of abelian CM-fields by using generalized Bernoulli numbers (see Theorem 4.17 in Introduction to cyclotomic fields by L. C. Washington, Grad. Texts in Math., vol. 83, Springer-Verlag, 1982). Here, we provide a technique for computing the relative class number of any CM-field. 1. Statement of the results Proposition 1. Let n ≥ 1...
متن کاملExponents of the ideal class groups of CM number fields
Since class numbers of CM number fields of a given degree go to infinity with the absolute values of their discriminants, it is reasonable to ask whether the same conclusion still holds true for the exponents of their ideal class groups. We prove that under the assumption of the Generalized Riemann Hypothesis this is indeed the case. 1991 Mathematics Subject Classification. Primary 11R29, 11R21.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2010
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2009.09.013